Ugly Problem

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Everyone hates ugly problems.

You are given a positive integer. You must represent that number by sum of palindromic numbers.

A palindromic number is a positive integer such that if you write out that integer as a string in decimal without leading zeros, the string is an palindrome. For example, 1 is a palindromic number and 10 is not.

Input

In the first line of input, there is an integer T denoting the number of test cases.

For each test case, there is only one line describing the given integer s ($1\leq s \leq 10^{1000}$).

Output

For each test case, output “Case #x:” on the first line where x is the number of that test case starting from 1. Then output the number of palindromic numbers you used, n, on one line. n must be no more than 50. en output n lines, each containing one of your palindromic numbers. Their sum must be exactly s.

Sample Input

2 18 1000000000000

Sample Output

Case #1: 2 9 9 Case #2: 2 999999999999 1
Hint
9 + 9 = 18 999999999999 + 1 = 1000000000000

Hint

wange2014

Source

2016中国大学生程序设计竞赛(长春)-重现赛

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